Lower types of δ-subharmonic functions of the nonintegral order

Abstract

It is proved that the lower types of functions $T (r, u)$ and $N (r, u) = N (r, u_1) - N (z, u_2)$ relative to the proximate order $\rho(r)$ of a function $u=u_1-u_2$ of fractional order $\rho$  $δ$-subharmonic in $\mathbb {R}^m$, $m\geq2$, coincide, that is, are simultaneously minimal or mean. In the case of an arbitrary proximate order $\rho(r)$ the assertion is, in general, false.